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Parikh vectors
3ZNM_1 6URX_1 2PAE_1 Letter Amino acid
18 15 4 P Proline
13 14 8 Y Tyrosine
9 2 3 C Cysteine
24 23 14 I Isoleucine
22 2 12 K Lycine
10 14 6 F Phenylalanine
29 17 9 N Asparagine
10 4 4 H Histidine
25 22 9 L Leucine
6 1 1 W Tryptophan
18 15 11 V Valine
14 8 11 D Aspartic acid
6 4 4 M Methionine
26 19 8 S Serine
21 17 3 T Threonine
18 17 9 G Glycine
14 24 6 A Alanine
12 21 5 R Arginine
12 14 3 Q Glutamine
19 15 11 E Glutamic acid 

3ZNM_1|Chains A, C, E|HAEMAGGLUTININ|INFLUENZA A VIRUS (644788)
>6URX_1|Chain A|Ricin|Ricinus communis (3988)
>2PAE_1|Chains A, B|DTDP-6-deoxy-3,4-keto-hexulose isomerase|Aneurinibacillus thermoaerophilus (143495)
Protein code \(c\) LZ-complexity \(\mathrm{LZ}(w)\) Length \(n=|w|\) \(\frac{\mathrm{LZ}(w)}{n /\log_{20} n}\) \(p_w(1)\) \(p_w(2)\) \(p_w(3)\) Sequence \(w=f(c)\)
3ZNM , Knot 145 326 0.85 40 211 316 
DQICIGYHANNSTEQVDTIMEKNVTVTHAQDILEKTHNGKLCDLDGVKPLILRDCSVAGWLLGNPMCDEFINVPEWSYIVEKANPVNDLCYPGDFNDYEELKHLLSRINHFEKIQIIPKSSWSSHEASLGVSSACPYQGKSSFFRNVVWLIKKNSTYPTIKRSYNNTNQEDLLVLWGIHHPNDAAEQTKLYQNPTTYISVGTSTLNQRLVPRIATRSKVNGQSGRMEFFWTILKPNDAINFESNGNFIAPEYAYKIVKKGDSTIMKSELEYGNCNTKCQTPMGAINSSMPFHNIHPLTIGECPKYVKSNRLVLATGLRNSPQRETR
6URX , Knot 116 268 0.80 40 171 260 
MIFPKQYPIINFTTAGATVQSYTNFIRAVRGRLTTGADVRHEIPVLPNRVGLPINQRFILVELSNHAELSVTLALDVTNAYVVGYRAGNSAYFFHPDNQEDAEAITHLFTDVQNRYTFAFGGNYDRLEQLAGNLRENIELGNGPLEEAISALYYYSTGGTQLPTLARSFIICIQMISEAARFQYIEGEMRTRIRYNRRSAPDPSVITLENSWGRLSTAIQESNQGAFASPIQLQRRNGSKFSVYDVSILIPIIALMVYRCAPPPSSQF
2PAE , Knot 69 141 0.80 40 110 135 
GHMENKVINFKKIIDSRGSLVAIEENKNIPFSIKRVYYIFDTKGEEPRGFNAHKKLEQVLVCLNGSCRVILDDGNIIQEITLDSPAVGLYVGPAVWHEMHDFSSDCVMMVLASDYYDETDYIRQYDNFKKYIAKINLEKEG

Let \(P_w(n)\) be the set of distinct subwords (intervals) in a word \(w\). Let \(p_w(n)\) be the cardinality of \(P_w(n)\). Let \(f(c)\) be the sequence in FASTA with 4-symbol Protein Data Bank code \(c\).

\(|P_{f(3ZNM_1)}(2) \setminus P_{f(6URX_1)}(2)|=112\), \(|P_{f(6URX_1)}(2) \setminus P_{f(3ZNM_1)}(2)|=72\). Let \( Z_k(x,y)=|P_x(k)\setminus P_y(k)|+|P_y(k)\setminus P_x(k)| \) be a LZ76 style (set of subwords) Jaccard distance numerator for \(P(k)\).Hydrophobic-polar version of Sequence 1:00101100100000010011000101001001100000101001011011110000111111101100011011010011001011001001101000001001100100100101110001000010111001010010001100111110000001010000000000011111110010011000010001000101100010001110110000101001010111011010011010001011110010011001000110001001000000001111100011100101101100100100001111011000100000
Pair \(Z_2\) Length of longest common subsequence
3ZNM_1,6URX_1 184 4
3ZNM_1,2PAE_1 203 3
6URX_1,2PAE_1 171 3

Newick tree

 
[
	3ZNM_1:10.36,
	[
		6URX_1:85.5,2PAE_1:85.5
	]:14.86
]

Let d be the Otu--Sayood distance d.
Let d1 be the Otu--Sayood distance d1. (This makes the 4TYN sequence AAAAAA a close match...)
A roughly speaking expected distance is \((0.85)(0.8)(\frac{594 }{\log_{20} 594}-\frac{268}{\log_{20}268})=91.8\)
Status Protein1 Protein2 d d1/2
Query variables 3ZNM_1 6URX_1 122 108
Was not able to put for d
Was not able to put for d1

In notation analogous to [Theorem 16, Kjos-Hanssen, Niraula and Yoon (2022)],
\[ \delta= \alpha \mathrm{min} + (1-\alpha) \mathrm{max}= \begin{cases} d &\alpha=0,\\ d_1/2 &\alpha=1/2 \end{cases} \]